What is heat?

I know heat as the average kinetic energy of the particles in a system, is this correct? And that heat is transferred by transferring energy, which causes particles to go slower/faster, is this correct?

But what exactly is heat? Is heat made up of smaller particles, such as light is photons? I still don't really understand what exactly heat is.

Also, in vacuum, heat is through neutrinos, they carry the energy, is this right? Do photons in vacuum also transfer heat?

Not exactely. Temperature is a measure for the mean kinetic energy of the particles. Heat is the transfer of energy due to a temperature difference and it corrisponds to a change of entropy (depending on the temperature).

I don't think that generally heat consists out of particles like photons, but radiation does (what would be the only possible form of energy transfer due to a temperature difference (heat) in a vacuum).

Another way to think of heat is as work being done on a microscopic level, so as particles transferring their energy to other particles. Heat does not refer to the particles themselves, but to the transfer of energy.